Prove Equal Intercept theorem. solve it with steps. because it is a project work
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Answer:
The theorem states if a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts. It means that given any three mutually perpendicular lines, a line passing through them forms intercepts in the corresponding ratio of the distances between the lines.
For example, Suppose there are three lines, l, m and n. Keep the distance between l–m twice than the distance between m–n. So any line passing through them, the intercept made by l-m on the line is twice the intercept made by m-n.
In the figure given above, XY is a transversal cutting the line L1 and L2 at P and Q respectively. The line segment PQ is called the intercept made on the transversal XY by the lines L1 and L2.
In the figure given above, XY is a transversal cutting the line L1 and L2 at P and Q respectively. The line segment PQ is called the intercept made on the transversal XY by the lines L1 and L2.If a transversal makes equal intercepts on three or more parallel lines then any other transversal cutting them will also make equal intercepts.
In the figure given above, XY is a transversal cutting the line L1 and L2 at P and Q respectively. The line segment PQ is called the intercept made on the transversal XY by the lines L1 and L2.If a transversal makes equal intercepts on three or more parallel lines then any other transversal cutting them will also make equal intercepts.Given: Let there be three straight lines L1, L2, and L3 such that L1 ∥ L2 ∥ L3.
To Prove: KM = MN.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.2. By converse of Midpoint Theorem.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.2. By converse of Midpoint Theorem.3. PO = ON and OM ∥ L1.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.2. By converse of Midpoint Theorem.3. PO = ON and OM ∥ L1.3. By statement 2 and given.
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.2. By converse of Midpoint Theorem.3. PO = ON and OM ∥ L1.3. By statement 2 and given.4. M is the midpoint of NK, i.e., KM = MN (Proved)
To Prove: KM = MN.Construction: Join PN which cuts the L2 at O. Statement Reason1. PQ = QR and QO ∥ line L3.1. Given.2. O is the midpoint of PN, i.e., PO = ON.2. By converse of Midpoint Theorem.3. PO = ON and OM ∥ L1.3. By statement 2 and given.4. M is the midpoint of NK, i.e., KM = MN (Proved)4. By converse of Midpoint Theorem.
Ex-Q In the figure, all measurements are indicated in centimetre. Find the length of AO if AX =9.5 cm.
Solution: D. Given in the figure AD = DB = 4
AE =EC = 6
Then D and E are the midpoints of sides AB and AC respectively.
Thus, DE bisects AX at point O
∴ AO = 1/2 AX = 1/2 × 9.5 = 4.75
Hence the length of AO = 4.75
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